When we teach mathematics in college, we find a lot of mistakes, fallacies and flaws in the solution of the students. In this paper, we presented a variety of examples of mistakes and fallacies, including wrong proofs, misinterpreted definitions and the mistaken use of theory. The examples, taken from different classes and subjects, are based on our own experience of teaching mathematics. As the previous research argued, such mistakes, fallacies and flaws should be considered as natural phenomena in the students' progress and should be analyzed systematically for the more effective education. By providing a wide-ranging examples of mistakes and fallacies, and detailed analyses of them, we emphasized the significance of the analysis of mistakes and fallacies and proposed that more careful attention should be paid on the collection and development of teaching materials in the area of mistake and fallacy analysis. We hope that this study would be a meaningful contribution to the teaching of mathematics in college.

The purpose of this paper is to analyze teaching-learning program which can be applied to mathematically gifted students in primary school, Our program is based on constructivist views on teaching and learning of mathematics. Mainly, we study the algorithmic thinking of mathematically gifted students in primary school in connection with the network problems; Eulerian graph problem, the minimum connector problem, and the shortest path problem, The above 3-subjects are not familiar with primary school mathematics, so that we adapt teaching-learning model based on the social constructivism. To achieve the purpose of this study, seventeen students in primary school participated in the study, and video type(observation) and student's mathematical note were used for collecting data while the students studied. The results of our study were summarized as follows: First, network problems based on teaching-learning model of constructivist views help students learn the algorithmic thinking. Second, the teaching-learning model based on constructivist views gives an opportunity of various mathematical thinking experience. Finally, the teaching-learning model based on constructivist views needs more the ability of teacher's research and the time of teaching for students than an ordinary teaching-learning model.

This study analyzes the theoretical background concerning problem solving, mathematization and real-life problems. Further it examines how middle school mathematics teachers and high school students of first grade recognize the real-life problems provides in textbooks concerning the area of geometry. Following those results found from this analysis, this paper reveals the issues and problems that we noticed through the analysis of real-life problems from textbooks, level 8 and level 9, Also we suggest the application of them along with the development of real-life problems for students' uplifting problem solving skills.

We can use R package as a statistical package on the education of probability and statistics in elementary, middle and high school mathematics. R is an interactive mode package and graphical presentation tools in R are powerful. The greatest advantage is that R is a general public license package. We need to consider R package as a standard statistical package on the education of probability and statistics in elementary, middle and high school mathematics.

We described the overall explanation about R statistical package in Jang(2007). With referring the contents of the 7th national mathematics curriculum, we suggest the plan for applications of R package on probability and statistics education in elementary, middle and high school mathematics.

Producing tools for actively meeting social needs in a radical changing society due to the development of modern technology has been shifted from physical ability to intelligent ability. The prominence of educating creativity is perceived as a good preparation in order to deal with them. Considered that assessment which is systematic activity to collect, analyze, diagnose, and judge information of a series of instruction practices is means to impart evidence and feedback of teaching learning practices, education and assessment is placed on reciprocal relationship. Nevertheless, there has been some tendency of neglect of assessment, comparing education for upbringing creativity. In this paper model of pencil and paper problem is discussed focusing on the sub-components of creativity and problem solving as one of the variety of means to extend mathematical creativity.

It is said that the university mathematics education in Korea faces critical situations due to the decreases of both qualities and quantities of students. In this paper we examine college students in order to know their basic ability for understanding about fundamental functions, such as polynomial, trigonometric, logarithm and exponential functions which have learned from highschool mathematics courses. The subject are 354 freshmen of 4 universities located in Daejeon and Chongchung area. The result of this study shows as follows. i ) More than half students are not able to draw graphs of given functions, except polynomial. ii ) More students do not fully understand about function properties such as domain, codomain, range, max and min value, cycle and parallel translation.

The purpose of this study is to develop a tool which can be used in factor analysis of inequality on mathematics scholastic achievement. The objectives for study are as follows: First, we develop a model for 'factor analysis of inequality on mathematics scholastic achievement' transformed from Persell's 'A model for factor analysis of inequality on education'. Second, we analyze the inequality factors with the deviation index of objects on mathematics scholastic achievement that we have developed. The results of this study are as follows: We development a model for 'factor analysis of inequality on Mathematics' and inequality factors on mathematics scholastic achievement in secondary schools are private education, scholarships of parents, region, sex and school system. The factors most influenced in mathematics scholastic achievement are economic standings of household, scholarships of parents and private educations in order.

The purpose of this study is to develop a tool which can be used in factor analysis of inequality on mathematics education. The objectives for study are develop an index that can be used to find a deviation of objects on mathematics scholastic achievement. The results of this study are deviation index of objects on mathematics scholastic achievement which development can be applications to Gini coefficient.

This research is aimed to inquiry retention types of middle school students about results of evaluation in school mathematics, For this purpose, we selected evaluation time, problem types, evaluation score, evaluation factors as important factors which influence to students' retention types. Then we classified students' retention types about results of evaluation in school mathematics. From this results, we selected two students as participants, and collected data through depth interviews of them. In depth interviews, we focused on 'what is the core factor influenced to students' evaluation', 'how the core factors reappear in the future'. Through this process, we analyzed middle school students' retention types about results of evaluation in school mathematics.

In this study, we made the analysis of the relation with mathematical tests and scholastic attainments of gifted students using the results of entrance end comprehensives exams and so on in science education center for gifted youths. For this, we firstly made an analysis of correlation between math and math, math and science and science and science using the test results. And then, we interviewed four students. From this, we found followings. First, in every assessment except for those carried out during the semester in the center, we saw a very low or negative correlation between the students' grades in math and that in science. Second, in contrast to the correlations among other assessments, a high correlation of the students' grades in math and science appeared in regard of the assessments carried out during the semester in the center. Third, correlations between the grades of assessments in mathematics were much lower than that in science. Fourth, many students thought the assessments in the center were not as valuable as those in their schools, which are referred to in getting into a school of high grade. So some of the students who gained excellent grades showed a relatively low achievement. Fifth, students in the center regarded a vigorous communication and inquiry learning on enriched themes as the biggest merit of attending the center.